Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.Scanner;
public class A{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int rows = sc.nextInt();
        int cols = sc.nextInt();
        int[] rowMin = new int[rows];
        int[] colMin = new int[cols];
        int rowMinimum;
        int colMinimum;
        int[][] numbers = new int[rows][cols];
        int currentInt;
        int[] firstMoves;
        int[] secondMoves;
        int totalMoves = 0;
        boolean impossible = false;
        for(int i = 0; i < rows; i++){
            for(int j = 0; j < cols; j++){
                currentInt = sc.nextInt();
                numbers[i][j] = currentInt;
                if(j == 0){
                    rowMin[i] = currentInt;
                }else{
                    if(currentInt < rowMin[i]){
                        rowMin[i] = currentInt;
                    }
                }
                if(i == 0){
                    colMin[j] = currentInt;
                }else{
                    if(currentInt < colMin[j]){
                        colMin[j] = currentInt;
                    }
                }
            }
        }
        sc.close();
        if(rows <= cols){
            for(int i = 0; i < rows; i++){
                for(int j = 0; j < cols; j++){
                    numbers[i][j]-= rowMin[i];
                }
            }
        }else{
            for(int i = 0; i < cols; i++){
                for(int j = 0; j < rows; j++){
                    numbers[j][i]-= colMin[i];
                }
            }
        }
        rowMinimum = rowMin[0];
        for(int i = 1; i < rowMin.length; i++){
            if(rowMin[i] < rowMinimum){
                rowMinimum = rowMin[i];
            }
        }
        colMinimum = colMin[0];
        for(int i = 0; i < colMin.length; i++){
            if(colMin[i] < colMinimum){
                colMinimum = colMin[i];
            }
        }
        //prepare move arrays
        if(rows <= cols){
            firstMoves = new int[rows];
            secondMoves = new int[cols];
            for(int i = 0; i < rows; i++){
                firstMoves[i] = rowMin[i];
                if(firstMoves[i] != 0) totalMoves+=firstMoves[i];
            }
            for(int i = 0; i < cols; i++){
                secondMoves[i] = colMin[i] - rowMinimum;
                if(secondMoves[i]!= 0) totalMoves+=secondMoves[i];
            }
        }else{
            firstMoves = new int[cols];
            secondMoves = new int[rows];
            for(int i = 0; i < cols; i++){
                firstMoves[i] = colMin[i];
                if(firstMoves[i] != 0) totalMoves+=firstMoves[i];
            }
            for(int i = 0; i < rows; i++){
                secondMoves[i] = rowMin[i] - colMinimum;
                if(secondMoves[i]!= 0) totalMoves+=secondMoves[i];
            }
        }
        //check for impossibility
        if(rows <= cols){
            //iterate through columns and check if subtraction returns 0 always
            for(int i = 0; i < cols; i++){
                for(int j = 0; j < rows; j++){
                    numbers[j][i] -= secondMoves[i];
                    if(numbers[j][i] != 0){
                        impossible = true;
                        break;
                    }
                }
            }
        }else{
            //iterate through rows...
            for(int i = 0; i < rows; i++){
                for(int j = 0; j < cols; j++){
                    numbers[i][j] -= secondMoves[i];
                    if(numbers[i][j] != 0){
                        impossible = true;
                        break;
                    }
                }
            }
        }
        if(impossible == true){
            System.out.println(-1);
        }else{
            System.out.println(totalMoves);
            if(rows <= cols){
                for(int i = 0; i < rows; i++){
                    if(firstMoves[i] > 0){
                        for(int j = 0; j < firstMoves[i]; j++){
                            System.out.println("row " + (i+1));
                        }
                    }
                }
                for(int i = 0; i < cols; i++){
                    if(secondMoves[i] > 0){
                        for(int j = 0; j < secondMoves[i]; j++){
                            System.out.println("col " + (i+1));
                        }
                    }
                }
            }else{
                for(int i = 0; i < cols; i++){
                    if(firstMoves[i] > 0){
                        for(int j = 0; j < firstMoves[i]; j++){
                            System.out.println("col " + (i+1));
                        }
                    }
                }
                for(int i = 0; i < rows; i++){
                    if(secondMoves[i] > 0){
                        for(int j = 0; j < secondMoves[i]; j++){
                            System.out.println("row " + (i+1));
                        }
                    }
                }
            }
        }
    }
}